# Probability distribution solutions of a general linear equation of infinite order, II

• Volume: 99, Issue: 3, page 215-224
• ISSN: 0066-2216

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## Abstract

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Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation $F\left(x\right)={\int }_{\Omega }F\left(\tau \left(x,\omega \right)\right)P\left(d\omega \right)$. We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.

## How to cite

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Tomasz Kochanek, and Janusz Morawiec. "Probability distribution solutions of a general linear equation of infinite order, II." Annales Polonici Mathematici 99.3 (2010): 215-224. <http://eudml.org/doc/281050>.

@article{TomaszKochanek2010,
abstract = {Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation $F(x) = ∫_Ω F(τ(x,ω)) P(dω)$. We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.},
author = {Tomasz Kochanek, Janusz Morawiec},
journal = {Annales Polonici Mathematici},
language = {eng},
number = {3},
pages = {215-224},
title = {Probability distribution solutions of a general linear equation of infinite order, II},
url = {http://eudml.org/doc/281050},
volume = {99},
year = {2010},
}

TY - JOUR
AU - Tomasz Kochanek
AU - Janusz Morawiec
TI - Probability distribution solutions of a general linear equation of infinite order, II
JO - Annales Polonici Mathematici
PY - 2010
VL - 99
IS - 3
SP - 215
EP - 224
AB - Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation $F(x) = ∫_Ω F(τ(x,ω)) P(dω)$. We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.
LA - eng
UR - http://eudml.org/doc/281050
ER -

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